Don, I asked the same question on one of the other forums, only my question was for the Sierra in general... not just Yosemite. I was given a Link showing the Average snow levels in the northern, central, and southern areas of the Sierra, and how this year compares to others.

Even with a heavy snow fall, the passes should all be passable by end of July or 1st week in August. By mid June, snow will be at the 11,000 level (eastern side). End of July there will be snow and ice with many footprints on many of the routes with trails. It might be a bit of an adventure in some cases (in early season, it might be worthwhile to take a 50' hank of 1/4" line to lower packs down to a trail buddy) but if you follow the foot prints of those who have gone ahead of you. You will be fine.